Attorney: Mel Gibson approaches prosecutors with a proposal

Gibson is under investigation for possible domestic violence against his ex-girlfriend

The ex-girlfriend is also being investigated for alleged extortion

Gibson and Oksana Grigorieva are in a bitter child custody fight

Los Angeles (CNN) -- Under investigation for possible domestic violence against his ex-girlfriend, actor Mel Gibson has approached Los Angeles County prosecutors "with a proposal that would bring all of this to an immediate end," his attorney, Blair Berk, said in a statement Wednesday.

"I know from almost 20 years as a criminal defense lawyer that sometimes justice can come for a client at too high a personal price. That is particularly so for Mel, whose right to due process can only be exercised in this case with an enormous media circus attached," Berk said.

"Mel's only priority throughout all of this has been that the best interests of his young daughter Lucia and the rest of his children be put first in any decisions made. It is with only that in mind that he asked me to approach the district attorney with a proposal that would bring all of this to an immediate end," Berk said in the statement.

Berk added there must be a court hearing where the proposal will be formally accepted by the court and that prosecutors would announce that court date.

Prosecutors are considering evidence gathered by sheriff's investigators to decide if a domestic violence case will be filed against Gibson because of an incident a year ago with his ex-girlfriend, Oksana Grigorieva.

Detectives are also investigating Gibson's charge that Grigorieva, a Russian musician, tried to extort money from him with recordings she made of his telephone calls, a Los Angeles County Sheriff's spokesman said.

The couple is in a bitter legal fight over custody of their three-year-old daughter. The sheriff's investigation findings have been in the hands of prosecutors since August.

Steve Jaffe, a representative for Grigorieva, told CNN that they "won't comment on the situation regarding Mr. Gibson."